The present invention relates to a method for predicting the lifetime of an insulating film for use in a semiconductor device and to a method for reliability testing of the device by utilizing the lifetime prediction method.
Hereinafter, a known lifetime prediction method for an insulating film will be described as being applied to the lifetime prediction of a gate insulating film for a MOSFET.
It should be noted that when a voltage or current value is preceded by a negative sign, that notation herein means that the potential level is lower at the gate electrode than at the substrate. Also, the xe2x80x9cdielectric breakdownxe2x80x9d herein means a steep rise of leakage current resulting from stressing, i.e., the generation of a hard breakdown (HBD), for a relatively thick insulating film, but means the generation of a soft breakdown (SBD) for a relatively thin insulating film. For a relatively thin insulating film, however, even if the SBD and HBD have occurred there at a time, it is supposed that only the SBD has occurred there.
First, an accelerating voltage (e.g., with an absolute value of 6 V), higher than an actual operating voltage normally applied (e.g., with an absolute value of 1.5 V), is applied to the gate electrode of a MOSFET under test, and a current flowing through its gate insulating film is measured. In this manner, a time it takes for the gate insulating film to cause a dielectric breakdown, i.e., the lifetime of the insulating film, is estimated (i.e., an accelerated test is performed). In this case, as the accelerating voltage is set even higher than the actual operating voltage, the insulating film lifetime, expected by the accelerated test, becomes even shorter than the lifetime of the insulating film under actual operating conditions.
Next, into a relationship between the voltage or electric field applied to the gate insulating film and the insulating film lifetime, i.e., a voltage-lifetime model (that should be made beforehand), the insulating film lifetime, expected by the accelerated test, is extrapolated. In this manner, the insulating film lifetime under actual operating conditions is calculated.
Hereinafter, a first problem of the known lifetime prediction method for an insulating film will be described.
In the known lifetime prediction method, a time it takes for the insulating film to cause a dielectric breakdown should be actually measured at an accelerated test. Thus, it takes a long time to predict the lifetime of the insulating film. However, if the difference between the accelerating and actual operating voltages is increased to shorten the time for predicting the insulating film lifetime, then the expected lifetime of the insulating film will have its accuracy decreased because the voltage-lifetime model becomes less reliable. Nevertheless, if the accelerated test is performed a great number of times with the accelerating voltage set closer to the actual operating voltage to predict the lifetime of the insulating film more accurately, then it takes an even longer time to predict the lifetime of the insulating film.
As described above, in predicting the lifetime of an insulating film, an accurate voltage-lifetime model should be prepared.
Hereinafter, xe2x80x9c1/Exe2x80x9d and xe2x80x9cExe2x80x9d models will be described as typical known voltage-lifetime models.
FIG. 12 illustrates a relationship between a stress voltage applied to the gate insulating film of an n-channel MOSFET and a total injected electron quantity QBD, i.e., a total quantity of electrons injected into the gate insulating film before the dielectric breakdown occurs there. FIG. 12 also illustrates a relationship between the stress voltage and a total injected hole quantity QP, i.e., a total quantity of holes injected into the gate insulating film before the dielectric breakdown occurs there. In this case, the thickness of the gate insulating film is 5 nm and the gate length and width are both 100 xcexcm. That is to say, the area of the gate insulating film is 0.01 mm2. In FIG. 12, the total injected electron and holes quantities QBD and QP are indicated by open and solid circles, respectively.
As shown in FIG. 12, the higher the stress voltage, the smaller the total injected electron quantity QBD. On the other hand, the total injected hole quantity QP is constant irrespective of the stress voltage. That the total injected hole quantity QP becomes constant, i.e., anode hole injection model, was already reported by C. Hu et al. See I. C. Chen, S. E. Holland and C. Hu: IEEE Trans. Elec. Dev. 32 (1985) p. 413 and J. C. Lee, I. C. Chen and C. Hu: IEEE Trans. Elec. Dev. 35 (1988) p. 2268, for example.
It should be noted that when I say xe2x80x9cconstantxe2x80x9d herein, this term also implies xe2x80x9csubstantially constantxe2x80x9d.
According to the anode hole injection model, the dielectric breakdown is believed to occur in the following manner. First, electrons, which have been injected from the cathode (e.g., gate electrode) into the gate insulating film due to stressing, create holes in the anode (e.g., substrate). Then, the holes created are injected back into the gate insulating film, thereby producing defects in the gate insulating film and eventually causing the dielectric breakdown there. In this case, the total injected hole quantity QP is believed to be constant until the dielectric breakdown occurs in the gate insulating film. The probability that the holes are created in the anode by the electrons and then injected into the gate insulating film is generally called a xe2x80x9cquantum efficiency xcex3xe2x80x9d, which greatly depends on the stress voltage. Thus, since a relationship QP=xcex3xc3x97QBD is met, the total injected electron quantity QBD changes with the quantum efficiency xcex3.
It is known that the lifetime TBD of the gate insulating film, predicted after the anode hole injection model, is exponentially proportional to the inverse of a stress electric field EOX (i.e., an electric field actually formed in the film due to the application of the stress voltage). For that reason, the anode hole injection model is also called a xe2x80x9c1/Exe2x80x9d model. The stress electric field EOX is given by:
EOX=(fraction of stress voltage applied to gate insulating film)÷(thickness of gate insulating film)
As opposed to the xe2x80x9c1/Exe2x80x9d model, the xe2x80x9cExe2x80x9d model (see, e.g., J. W. McPherson and D. A. Baglee: Int. Rel. Phys. Symposium (1985) p. 1) supposes that the stress electric field EOX itself degrades the gate insulating film and finally causes the dielectric breakdown there. See also J. W. McPherson and H. C. Mogul: J. Appl. Phys. 84 (1998) pp. 1513-1523.
FIG. 13 illustrates a relationship between the stress electric field EOX formed in the gate insulating film and the lifetime TBD of the film predicted after the xe2x80x9c1/Exe2x80x9d model and a relationship between the stress electric field EOX and the lifetime TBD predicted after the xe2x80x9cExe2x80x9d model. The data illustrated in FIG. 13, i.e., the lifetimes TBD of the gate insulating film predicted after the xe2x80x9c1/Exe2x80x9d and xe2x80x9cExe2x80x9d models, was collected from the same gate insulating film as that used for FIG. 12. And the predicted lifetimes of those films were fitted to each other, i.e., almost equal to each other at a stress electric field EOX in the range from 11 to 13 MV/cm.
As shown in FIG. 13, the lifetime TBD of the gate insulating film as predicted after the xe2x80x9c1/Exe2x80x9d model (see the dashed line) increases exponentially even in the semilogarithmic plot as the stress electric field EOX decreases. But the lifetime TBD of the gate insulating film as predicted after the xe2x80x9cExe2x80x9d model (see the solid line) shows a negative proportionality for the stress electric field EOX (in the semilogarithmic plot).
Hereinafter, a second problem of the known method for predicting the lifetime of an insulating film after the xe2x80x9c1/Exe2x80x9d or xe2x80x9cExe2x80x9d model, for example, will be described.
It has been impossible to definitely decide which should be regarded as the more appropriate voltage-lifetime model, xe2x80x9c1/Exe2x80x9d or xe2x80x9cExe2x80x9d. This is partly because if the difference between the insulating film lifetimes predicted after these models is to be actually recognized, then the insulating film lifetimes should be measured for stress electric fields in a very wide range.
Specifically, suppose the lifetime TBD of a gate insulating film is actually measured for a stress electric field EOX in the range from 11 to 13 MV/cm. And then the lifetime TBD for a stress electric field EOX of less than 11 MV/cm is predicted by applying the xe2x80x9c1/Exe2x80x9d and xe2x80x9cExe2x80x9d models shown in FIG. 13 to the lifetime TBD actually measured. In that case, no significant difference is recognizable between the lifetimes TBD predicted on these models until the stress electric field EOX is about 9 Mv/cm or less.
Accordingly, to know which is more appropriate, xe2x80x9c1/Exe2x80x9d or xe2x80x9cExe2x80x9d, the lifetime TBD of the gate insulating film should be actually measured for stress electric fields EOX in the range from 9 through 13 MV/cm. However, a lifetime TBD, corresponding to an electric field intensity in such a wide range, is changeable over six orders of magnitude or more. Also, a dielectric breakdown time, i.e., time to breakdown, or time it takes for the gate insulating film to cause a dielectric breakdown, is also variable over a wide range. Accordingly, the lifetime TBD should be predicted by measuring the dielectric breakdown times of a great number of sample gate insulating films and by processing the results of measurement statistically. In that case, to reduce the adverse effects of that variation, the lifetimes TBD should be actually measured for electric field intensities in an even broader range.
However, it is difficult to accurately measure the insulating film lifetime that is changeable over six orders of magnitude or more. For that reason, no one could ever definitely decide which is more appropriate, xe2x80x9c1/Exe2x80x9d or xe2x80x9cExe2x80x9d. As a result, the lifetime of an insulating film under actual operating conditions of a semiconductor device, i.e., the lifetime of an insulating film in which a weak electric field has been formed, could not be predicted reliably.
In view of these respects, a first object of the present invention is to predict the lifetime of an insulating film in a short time, and a second object thereof is to accurately predict the lifetime of an insulating film under actual operating conditions of a semiconductor device.
To achieve the first object, or to solve the first problem, the present inventor carried out the following research.
First, a MOSFET, in which a gate insulating film and a gate electrode were formed out of a silicon dioxide film and a polysilicon film, respectively, on a p-type silicon substrate, is prepared. In this case, the thickness of the gate insulating film is 6.0 nm and the area of the gate insulating film is 0.01 mm2, for example.
Next, a constant voltage of xe2x88x926.0 V is applied as a stress voltage to the gate electrode of the MOSFET (which will be herein called a xe2x80x9cMOSFET under testxe2x80x9d). Thereafter, every time a time interval T has passed, the application of the stress voltage is once suspended, a gate voltage VG (e.g., xe2x88x924.5 V) is applied to the gate electrode and then a gate current IG, flowing through the gate insulating film, is measured. The resultant relationships between the gate voltage VG and gate current IG, or I-V characteristics, are shown in FIG. 1. In FIG. 1, the I-V characteristics, corresponding to respective time intervals of 0, 1, 10, 100 and 1,000 seconds (which appear on the log scales at regular intervals), are illustrated.
As shown in FIG. 1, while the gate voltage VG is within a predetermined range, the longer the time interval T (i.e., as the stressing time passes), the larger the gate current IG. Specifically, suppose the gate voltage VG is equal to the stress voltage (i.e., xe2x88x926.0 V), for example. In that case, the gate current IG at the time of dielectric breakdown (corresponding to T=1,000 in the example illustrated in FIG. 1) is just several time greater than that at the initial stage of stressing (corresponding to T=0). On the other hand, if the gate voltage VG is xe2x88x924.5 V, for example, the gate current IG gradually increases with the passage of the stressing time. In the end, the gate current IG will have changed approximately by several orders of magnitude. Such a current, of which a considerable increase is observable between the initial stage of stressing and the time of dielectric breakdown, is called an A-mode SILC current (A-mode stress induced leakage current). In the example illustrated in FIG. 1, a gate current IG, corresponding to a gate voltage VG in the range from about xe2x88x923 to about xe2x88x925.5 V, is the A-mode SILC current.
FIG. 2 illustrates a relationship between the A-mode SILC current IA (for VG=xe2x88x924.5 V) shown in FIG. 1 and the stressing time TS (see the dashed line).
That is to say, the A-mode SILC current IA shown in FIG. 2 is measured in the following manner. First, a constant voltage stress of xe2x88x926.0 V is applied to the gate electrode of a MOSFET under test. Thereafter, every time a predetermined time interval has passed, the stressing is once suspended, a gate voltage VG of xe2x88x924.5 V is applied to the gate electrode and then the A-mode SILC current IA flowing through the gate insulating film is measured. In this case, the intensity of the stress electric field EOX formed in the gate insulating film is about 12.0 MV/cm.
FIG. 2 also illustrates a relationship between a gate current IG flowing through the gate insulating film at a gate voltage VG of xe2x88x926.0 V, i.e., an FN (Fowler-Nordheim) current IFN, and the stressing time TSD (see the solid line). The FN current IFN shown in FIG. 2 is measured in the following manner. First, a constant voltage stress of xe2x88x926.0 V is applied to the gate electrode of a MOSFET under test. Then, every time a predetermined time interval has passed, the FN current IFN, flowing through the gate insulating film, is measured. That is to say, in measuring the FN current IFN, stressing does not have to be suspended unlike the measurement of the A-mode SILC current IA because the stress voltage is equal to the gate voltage VG at xe2x88x926.0 V.
As shown in FIG. 2, as the stressing time TSD passes, the A-mode SILC current IA increases. However, in FIG. 2 (i.e., in a double logarithmic plot with the abscissa TSD and the ordinate IA), the slope of the time dependent variation of the A-mode SILC current IA starts to decline when the stressing time TSD reaches a polarity change time TAsat (i.e., when TAsat=18 seconds in the example illustrated in FIG. 2).
As also shown in FIG. 2, the FN current IFN goes on increasing with the passage of the stressing time TS until the stressing time TS reaches a saturation time TFNsat (i.e., TFNsat=85 seconds in the example illustrated in FIG. 2). However, once the stressing time TS exceeds the saturation time TFNsat, the FN current IFN decreases with the passage of the stressing time TS. In other words, the FN current IFN reaches its maximum value when the stressing time TS is the saturation time TFNsat.
As also shown in FIG. 2, when the stressing time TS reaches a dielectric breakdown time TBD (i.e., TBD=2,000 seconds in the example shown in FIG. 2), a dielectric breakdown occurs in the gate insulating film of the MOSFET under test.
FIG. 3 illustrates relationships between the A-mode SILC current IA (for VG=xe2x88x924.0 V) flowing through the gate insulating film and the stressing time TBD where various stress voltages are applied to the MOSFET under test (i.e., the gate electrode is at the lower potential level). That is to say, the relationships illustrated in FIG. 3 correspond to stress electric fields EOX of various intensities that have been formed in the gate insulating film of the MOSFET under test.
In FIG. 3, the variations of the A-mode SILC currents IA, corresponding to the respective stress electric fields EOX, with the passage of the stressing time TS are represented by open circles and dashed lines. The values of the A-mode SILC currents IA when the stressing times TS reach the respective polarity change times TAsat are indicated by solid squares. And the values of the A-mode SILC currents IA when the stressing times TS reach the respective dielectric breakdown times TBD are indicated by solid circles. However, if the stress electric field EOX (or the stress voltage) is small, then the amount of the A-mode SILC current IA is also small. As a result, current components other than the A-mode SILC current IA, which exist on the background, are dominating, and therefore, the behavior of the A-mode SILC current IA is not clear.
As shown in FIG. 3, there is a correspondence between the polarity change time Teat and the dielectric breakdown time TBD for each stress electric field EOX.
Although not shown, there is also a similar correspondence between the saturation time TFNsat and the dielectric breakdown time TBD for each stress electric field EOX.
FIG. 4 illustrates relationships between the stress electric field EOX and the polarity change time TAsat, saturation time TFNsat or dielectric breakdown time TBD that were obtained from the results shown in FIG. 3, for example. In FIG. 4, the polarity change times TAsat, saturation times TFNsat and dielectric breakdown times TBD, corresponding to predetermined stress electric fields EOX, are indicated by solid circles, solid squares and open circles, respectively.
As shown in FIG. 4, the lines, representing the correlations between the dielectric breakdown time TBD, polarity change time TAsat or saturation time TFNsat and the stress electric field EOX (see the dashed, solid and one-dot-chain lines, respectively), are substantially parallel to each other. In this case, if these correlations are plotted without using logarithmic scales for the ordinates (i.e., the times), then the graphs (or curves) representing those correlations will be equally spaced from each other.
Accordingly, by finding the correlation between the polarity change time TAsat or saturation time TFNsat and the stress electric field EOX and obtaining a first dielectric breakdown time TBD for a first stress electric field EOX a second dielectric breakdown time TBD can be estimated for a second stress electric field EOX. This method will be herein called a xe2x80x9cnondestructive lifetime prediction methodxe2x80x9d. Thus, the xe2x80x9cnondestructive lifetime prediction methodxe2x80x9d makes the dielectric breakdown time TBD estimable by measuring the polarity change time TAsat or saturation time TFNsat, which is much shorter than the dielectric breakdown time TBD in practice, without actually measuring the dielectric breakdown time TBD by an accelerated test.
To achieve the second object, i.e., to solve the second problem, the present inventor carried out the following research.
First, a MOSFET, in which a gate insulating film and a gate electrode were formed out of a silicon dioxide film and a polysilicon film, respectively, on a p-type silicon substrate, is prepared. In this case, the thickness of the gate insulating film is 5.0 nm and the area of the gate insulating film is 0.01 mm2, for example.
Next, a stress voltage is applied to the gate electrode of the MOSFET (which will be herein called a xe2x80x9cMOSFET under testxe2x80x9d). Then, a time that should pass after the stress started to be placed and before the gate insulating film causes a dielectric breakdown, i.e., insulating film lifetime TBD, is actually measured.
FIG. 5 illustrates relationships between the insulating film lifetime TBD, actually measured using the MOSFET under test, and the stress voltage. In FIG. 5, the insulating film lifetimes TBD actually measured are indicated by solid circles, and the insulating film lifetimes TBD, predicted after the xe2x80x9c1/Exe2x80x9d and xe2x80x9cExe2x80x9d models, are represented by the dashed and solid lines, respectively, for reference. It should be noted that the insulating film lifetimes TBD, predicted after the xe2x80x9c1/Exe2x80x9d and xe2x80x9cExe2x80x9d models, were fitted so as to match to the actually measured insulating film lifetime TBD best. Also, in predicting the insulating film lifetime TBD on the xe2x80x9c1/Exe2x80x9d model, the total injected hole quantity QP (constant value) shown in FIG. 12 was used.
As shown in FIG. 5, the insulating film lifetime TBD actually measured is closer to the insulating film lifetime TBD predicted after the xe2x80x9cExe2x80x9d model than to the insulating film lifetime TBD predicted after the xe2x80x9c1/Exe2x80x9d model. Specifically, where the stress voltage is about 6 V or less, the xe2x80x9cExe2x80x9d model is more accurate than the xe2x80x9c1/Exe2x80x9d model.
As also shown in FIG. 5, the insulating film lifetime TBD actually measured is shorter than the insulating film lifetime TBD predicted after the xe2x80x9c1/Exe2x80x9d model, i.e., supposing that the total injected hole quantity QP should be constant. This means that as the stress voltage decreases, the total injected hole quantity QP decreases in actuality.
Next, the total injected hole and electron quantities QP and QBD are derived from the insulating film lifetime TBD actually measured. Specifically, using the insulating film lifetime TBD actually measured for a predetermined stress voltage and a hole current Isub flowing through the gate insulating film at the predetermined stress voltage, the total injected hole quantity QP is obtained by QP=TBDxc3x97Isub, for example. As for the MOSFET under test, the hole current Isub represents a quantity of holes contained in a substrate current flowing through the gate insulating film per unit time for the predetermined stress voltage. Also, using the insulating film lifetime TBD actually measured for the predetermined stress voltage and an electron current IG flowing through the gate insulating film at the predetermined stress voltage, the total injected electron quantity QBD is obtained by QBD=TBDxc3x97IG, for example. As for the MOSFET under test, the electron current IG represents a quantity of electrons contained in a gate current flowing through the gate insulating film per unit time for the predetermined stress voltage.
FIG. 6 illustrates relationships between the total injected hole or electron quantity QP or QBD, calculated from the (actually measured) insulating film lifetime TBD shown in FIG. 5, and the stress voltage.
As shown in FIG. 6, if the stress voltage is higher than about 6 V (absolute value), then the total injected hole quantity QP is constant. Alternatively, if the stress voltage is lower than about 6 V (absolute value), then the quantity QP decreases with the fall of the stress voltage.
On the other hand, as also shown in FIG. 6, if the stress voltage is higher than about 6 V (absolute value), then the total injected electron quantity QBD decreases with the rise of the stress voltage. Alternatively, if the stress voltage is lower than about 6 V (absolute value), then the quantity QBD is constant.
That is to say, as the stress voltage decreases, the parameter being constant alternates from the total injected hole quantity QP into the total injected electron quantity QBD.
Also, in the example illustrated in FIG. 6 (where the area of the gate insulating film, or the gate area, is 0.01 mm2), a total injected hole quantity QP, which has reached a constant value against the variation in stress voltage, is about 10xe2x88x922 C/cm2. This constant value will be herein called a xe2x80x9ccritical injected hole quantity QPcritxe2x80x9d. And a total injected electron quantity QBD, which has reached a constant value against the variation in stress voltage, is about 103 C/cm2. This constant value will be herein called a xe2x80x9ccritical injected electron quantity QBDcritxe2x80x9d. That is to say, the critical injected electron quantity QBDcrit is greater than the critical injected hole quantity QPcrit approximately by four to five orders of magnitude.
Next, by using only the critical injected electron quantity QBDcrit corresponding to the total injected electron quantity QBD obtained from the insulating film lifetime TBD actually measured, a first provisional lifetime TBDe of the gate insulating film is obtained. In other words, the first provisional lifetime TBDe is obtained after an xe2x80x9celectron dominating modelxe2x80x9d that supposes electrons alone should degrade the gate insulating film. In this case, the following Equation
TBDe=QBDcrit/IGxe2x80x83xe2x80x83(1)
where IG is an electron current flowing through the gate insulating film at the predetermined stress voltage, may be used, for example.
Also, by using only the critical injected hole quantity QPcrit corresponding to the total injected hole quantity QP obtained from the insulating film lifetime TBD actually measured, a second provisional lifetime TBDh of the gate insulating film is obtained. In other words, the second provisional lifetime TBDh is obtained after a xe2x80x9chole dominating modelxe2x80x9d that supposes holes alone should degrade the gate insulating film, i.e., after the xe2x80x9c1/Exe2x80x9d model. In this case, the following Equation
TBDh=QPcrit/Isubxe2x80x83xe2x80x83(2)
where Isub is a hole current flowing through the gate insulating film at the predetermined stress voltage, may be used, for example.
FIG. 7 illustrates relationships between the first or second provisional lifetime TBDe or TBDh, obtained from the critical injected electron or hole quantity QBDcrit or QPcrit shown in FIG. 6, respectively, and the stress voltage.
In FIG. 7, the first provisional lifetimes TBDe, predicted after the xe2x80x9celectron dominating modelxe2x80x9d, are indicated by open circles, while the second provisional lifetimes TBDh, predicted after the xe2x80x9chole dominating modelxe2x80x9d, are indicated by open squares. In addition, the insulating film lifetime TBD, predicted after the xe2x80x9cExe2x80x9d model, is also represented in FIG. 7 by the solid line for reference.
Actually, though, both holes and electrons degrade the gate insulating film. Thus, strictly speaking, the real insulating film lifetime TBD should be predicted by the following Equation (3):
1/TBD=1/TBDe+1/TBDhxe2x80x83xe2x80x83(3)
Particularly when the first and second provisional lifetimes TBDe and TBDh are approximately on the same order, i.e., where electrons and holes contribute to the degradation of the gate insulating film to almost the same degrees (i.e., around 5.5 V in FIG. 7), the insulating film lifetime TBD is preferably predicted by Equation (3).
On the other hand, if there is a big difference between the first and second provisional lifetimes TBDe and TBDh, then the insulating film lifetime TBD can be approximated by the smaller one (i.e., the shorter lifetime) of the first and second provisional lifetimes TBDe and TBDh.
Thus, the results shown in FIG. 7 told me that an appropriate voltage-lifetime model should be as follows. Specifically, where the stress voltage is relatively high, such a model should suppose degradation of the gate insulating film due to holes (i.e., the second provisional lifetime TBDh) determines the insulating film lifetime TBD. On the other hand, where the stress voltage is relatively low, such a model should suppose degradation of the gate insulating film due to electrons (i.e., the first provisional lifetime TBDe) determines the insulating film lifetime TBD. That model will be herein called a xe2x80x9cDCC (dominant carrier change)xe2x80x9d model.
FIG. 8 illustrates a relationship between the insulating film lifetime TBD, which has been predicted for the MOSFET under test after the xe2x80x9cDCCxe2x80x9d model, and the stress voltage (see the solid line). In FIG. 8, relationships between the insulating film lifetime TBD, predicted after the xe2x80x9c1/Exe2x80x9d or xe2x80x9cExe2x80x9d model, and the stress voltage are represented by the dashed and one-dot-chain lines, respectively, for reference.
As shown in FIG. 8, where the stress voltage is in the range from 4 to 6 V, the insulating film lifetime TBD predicted after the xe2x80x9cDCCxe2x80x9d model is shorter than the insulating film lifetime TBD predicted after the xe2x80x9c1/Exe2x80x9d model.
As also shown in FIG. 8, if the stress voltage is about 4 V or less, the insulating film lifetime TBD predicted after the xe2x80x9cDCCxe2x80x9d model is longer than the insulating film lifetime TBD predicted after the xe2x80x9cExe2x80x9d model. Specifically, at stress voltages of about 4 V or less, as the stress voltage decreases, the insulating film lifetime TBD predicted after the xe2x80x9cExe2x80x9d model increases linearly in the semilogarithmic plot. On the other hand, as the stress voltage decreases, the insulating film lifetime TBD predicted after the xe2x80x9cDCCxe2x80x9d model increases steeply and exponentially even in the semilogarithmic plot.
In recent years, there have been many reports demonstrating the appropriateness of the xe2x80x9cExe2x80x9d model empirically. However, I believe that the xe2x80x9cExe2x80x9d model has been observed as an accurate one within the time range of the insulating film lifetime actually measured just because where the stress voltage is relatively low, it has been impossible to measure the insulating film lifetime within an actually measurable time range. For example, in FIG. 8, the insulating film lifetime is immeasurable for a stress voltage of about 4 V or less.
A first inventive method for predicting the lifetime of an insulating film was made based on the above-described findings, or by the xe2x80x9cnondestructive lifetime prediction methodxe2x80x9d, in particular.
Specifically, the first inventive lifetime prediction method is adapted to predict the lifetime of an insulating film for use in a semiconductor device, in which a time it takes for the insulating film to cause a dielectric breakdown is estimated as an expected lifetime of the insulating film. The method includes the step of finding a correlation between a stress condition imposed on an insulating film under test and a time it takes for the slope of a time dependent variation of an A-mode stress induced leakage current to start to decline in a double logarithmic plot or a correlation between the stress condition and a time it takes for an FN current to start to decrease. The insulating film under test has the same specification as the insulating film. The A-mode stress induced leakage current and the FN current both flow through the insulating film under test. The method further includes the step of actually measuring a first dielectric breakdown time it takes for the insulating film under test to cause the dielectric breakdown with a first stress condition imposed on the insulating film under test. And the method further includes the step of estimating, from the correlation and the first dielectric breakdown time, a second dielectric breakdown time it takes for the insulating film, on which a second stress condition is imposed, to cause the dielectric breakdown.
In the first lifetime prediction method, a correlation between a time it takes for the slope of a time dependent variation of an A-mode stress induced leakage current to start to decline (i.e., the polarity change time TAsat) in a double logarithmic plot and a stress condition is found. Or a correlation between a time it takes for an FN current to start to decrease (i.e., the saturation time TFNsat) and the stress condition is found. Next, a first dielectric breakdown time is actually measured for an insulating film under test, on which a first stress condition is imposed. Then, by reference to the correlation between the polarity change time TAsat or saturation time TFNsat and the stress condition, a second dielectric breakdown time is estimated from the first dielectric breakdown time for the insulating film on which a second stress condition is imposed. Accordingly, there is no need to actually measure the dielectric breakdown time of the insulating film under test by performing an accelerated test. As a result, the lifetime of the insulating film can be predicted in a shorter time.
Also, according to the first lifetime prediction method, the lifetime of a gate insulating film is predicted by using the polarity change time TAsat or saturation time TFNsatand the dielectric breakdown time that have been obtained by an accelerated test. Thus, compared to the known method using only the dielectric breakdown time obtained by an accelerated test, the lifetime of the gate insulating film can be predicted more accurately.
In the first lifetime prediction method, the stress condition is preferably a stress voltage or a stress electric field.
Then, the correlation between the polarity change time TAsat or saturation time TFNsat and the stress condition can be found just as intended.
In the first lifetime prediction method, the thickness of the insulating film is preferably 10 nm or less.
In such an embodiment, the A-mode stress induced leakage current or FN current can be measured accurately enough.
In t he first lifetime prediction method, the insulating film is preferably a gate insulating film for an MOS device.
In such an embodiment, the lifetime of the gate insulating film can be accurately predicted in a short time.
A second inventive method for predicting the lifetime of an insulating film was made based on the above-described findings, or after the xe2x80x9cDCCxe2x80x9d model, in particular.
Specifically, the second inventive lifetime prediction method is adapted to predict the lifetime of an insulating film for use in a semiconductor device, in which a time it takes for the insulating film to cause a dielectric breakdown is estimated as an expected lifetime of the insulating film. The method includes a first step of obtaining, as a critical injected electron quantity, a total injected electron quantity that has reached a constant value against a variation in stress voltage applied to the insulating film. The total injected electron quantity is a total quantity of electrons injected into the insulating film before the film causes the breakdown. The method also includes a second step of estimating, as the expected lifetime of the insulating film, a time it should take for a total quantity of electrons, injected into the insulating film under actual operating conditions of the device, to reach the critical injected electron quantity.
In the second lifetime prediction method, a total injected electron quantity (i.e., a total quantity of electrons injected into an insulating film before the film causes a dielectric breakdown) that has reached a constant value against a variation in stress voltage applied to the film is obtained as a critical injected electron quantity. Then, a time it should take for a total quantity of electrons, injected into the insulating film under actual operating conditions of the device, to reach the critical injected electron quantity is estimated as the expected lifetime of the insulating film.
Thus, compared to the known method (e.g., the xe2x80x9c1/Exe2x80x9d or xe2x80x9cExe2x80x9d model) for predicting the lifetime from the critical injected hole quantity or stress electric field, the lifetime of an insulating film under actual operating conditions of a semiconductor device can be predicted more accurately. That is to say, the lifetime of an insulating film, in which a weak electric field has been formed, can be predicted accurately enough.
Also, according to the second lifetime prediction method, the lifetime of the insulating film, predicted under the actual operating conditions of the device, is longer than the lifetime predicted by the known xe2x80x9cExe2x80x9d model method. Thus, an increased margin is available for the thickness of the insulating film or fabrication process conditions, for example. That is to say, the thickness of the insulating film or the fabrication process conditions, which have been non-applicable to the fabrication of semiconductor devices, are now applicable in the present invention. As a result, the performance of semiconductor devices, like the operating speeds thereof, can be improved.
In the second lifetime prediction method, the first step preferably includes the steps of actually measuring a dielectric breakdown time it takes for an insulating film under test, having the same specification as the insulating film, to cause the dielectric breakdown by applying a stress voltage to the insulating film under test; and then obtaining the total injected electron quantity using the dielectric breakdown time actually measured and an electron current flowing through the insulating film under test when the stress voltage is applied thereto.
In this manner, the total injected electron quantity can be estimated accurately.
In the second lifetime prediction method, the second step preferably includes the step of deriving the expected lifetime of the insulating film by
TBD=QBDcrit/IG
where TBD is the lifetime of the insulating film, QBDcrit is the critical injected electron quantity and IG is the amount of the electron current flowing through the insulating film under the actual operating conditions of the device.
In this manner, the lifetime of the insulating film can be predicted easily.
In the second lifetime prediction method, the first step preferably includes the step of obtaining, as a critical injected hole quantity, a total injected hole quantity that has reached a constant value against the variation in stress voltage applied to the insulating film. The total injected hole quantity is a total quantity of holes injected into the insulating film before the film causes the breakdown. And the first step preferably further includes the step of deriving the critical injected electron quantity from the critical injected hole quantity after that.
In such an embodiment, the critical injected electron quantity can be obtained without calculating the total injected electron quantity. Thus, the lifetime of an insulating film can be predicted easily.
In this particular embodiment, the step of obtaining the critical injected hole quantity in the first step preferably includes the steps of: actually measuring a dielectric breakdown time it takes for an insulating film under test, having the same specification as the insulating film, to cause the dielectric breakdown by applying a stress voltage to the insulating film under test; and then deriving the total injected hole quantity from the dielectric breakdown time actually measured and a hole current flowing through the insulating film under test when the stress voltage is applied thereto.
In this manner, the total injected hole quantity can be estimated accurately.
Alternatively, the step of obtaining the critical injected hole quantity in the first step may include the step of finding a correlation between a stress voltage applied to an insulating film under test and a time it takes for the slope of a time dependent variation of an A-mode stress induced leakage current to start to decline in a double logarithmic plot. The insulating film under test has the same specification as the insulating film. The A-mode stress induced leakage current flows through the insulating film under test. The step may further include the step of actually measuring a first dielectric breakdown time it takes for the insulating film under test to cause the dielectric breakdown with a first stress voltage applied to the insulating film under test. The step may further include the step of estimating, from the correlation and the first dielectric breakdown time, a second dielectric breakdown time it takes for the insulating film, to which a second stress voltage is applied, to cause the dielectric breakdown. And the step may further include the step of deriving the total injected hole quantity from the second dielectric breakdown time and a hole current flowing through the insulating film under test when the second stress voltage is applied thereto.
In this manner, the total injected hole quantity can be obtained in a short time.
In the second lifetime prediction method, the lifetime of the insulating film, which is estimated in the second step, is preferably regarded as a first provisional lifetime. And the method preferably further includes a third step of obtaining, as a critical injected hole quantity, a total injected hole quantity that has reached a constant value against the variation in stress voltage applied to the insulating film. The total injected hole quantity is a total quantity of holes injected into the insulating film before the film causes the breakdown. The method preferably further includes a fourth step of estimating, as a second provisional lifetime of the insulating film, a time it takes for a total quantity of holes, injected into the insulating film under the actual operating conditions of the device, to reach the critical injected hole quantity. And the method preferably further includes a fifth step of predicting the lifetime of the insulating film from the first and second provisional lifetimes.
In this manner, the lifetime of the insulating film can be predicted exactly.
In this particular embodiment, the third step preferably includes the step of actually measuring a dielectric breakdown time it takes for an insulating film under test, having the same specification as the insulating film, to cause the dielectric breakdown by applying a stress voltage to the insulating film under test. And the third step preferably further includes the step of deriving the total injected hole quantity from the dielectric breakdown time actually measured and a hole current flowing through the insulating film under test when the stress voltage is applied thereto.
In this manner, the total injected hole quantity can be estimated accurately.
Alternatively, the third step may include the step of finding a correlation between a stress voltage applied to an insulating film under test and a time it takes for the slope of a time dependent variation of an A-mode stress induced leakage current to start to decline in a double logarithmic plot. The insulating film under test has the same specification as the insulating film. The A-mode stress induced leakage current flows through the insulating film under test. The third step may further include the step of actually measuring a first dielectric breakdown time it takes for the insulating film under test to cause the dielectric breakdown with a first stress voltage applied to the insulating film under test. The third step may further include the step of estimating, from the correlation and the first dielectric break down time, a second dielectric breakdown time it takes for the insulating film, to which a second stress voltage is applied, to cause the dielectric breakdown. And the third step may further include the step of deriving the total injected hole quantity from the second-dielectric breakdown time and a hole current flowing through the insulating film under test when the second stress voltage is applied thereto.
In this manner, the total injected hole quantity can be obtained in a short time.
As another alternative, the fourth step may include the step of obtaining the second provisional lifetime by
TBDh=QPcrit/Isub
where TBDh is the second provisional lifetime, QPcrit is the critical injected hole quantity and Isub is the amount of the hole current flowing through the insulating film under the actual operating conditions of the device.
In such an embodiment, the second provisional lifetime can be obtained easily.
As yet another alternative, the fifth step may include the step of predicting the lifetime of the insulating film by
1/TBD=1/TBDe+1/TBDh
where TBD is the lifetime of the insulating film, TBDe is the first provisional lifetime and TBDh is the second provisional lifetime.
In this manner, the lifetime of the insulating film can be predicted easily.
An inventive method for reliability testing of a semiconductor device is adapted to test the reliability of a semiconductor device by estimating a time it takes for an insulating film for use in the device to cause a dielectric breakdown. The method includes a first step of obtaining, as a critical injected electron quantity, a total injected electron quantity that has reached a constant value against a variation in stress voltage applied to the insulating film. The total injected electron quantity is a total quantity of electrons injected into the insulating film before the film causes the breakdown. The method further includes a second step of estimating a first time it takes for a total quantity of electrons, injected into the insulating film under actual operating conditions of the device, to reach the critical injected electron quantity. If the first time is equal to or greater than a predetermined value, the method further includes third and fourth steps. The third step includes estimating a second time it takes for a first insulating film under test to cause a dielectric breakdown by applying a test voltage, higher than a voltage applied to the insulating film under the actual operating conditions of the device, to the first insulating film under test. The first insulating film under test has the same specification as the insulating film. The third step further includes determining, by the second time, a reference control level for a preselected control point of the insulating film after that. The fourth step includes applying the test voltage to a second insulating film under test, which also has the same specification as the insulating film, to measure the control point of the second insulating film under test. The fourth step further includes determining whether or not a result of the measurement meets the reference control level after that.
In the inventive reliability testing method, the reliability of a semiconductor device can be tested using the first time, i.e., the lifetime of the insulating film at an actual operating voltage as predicted by the second lifetime prediction method of the present invention. Thus, compared to the known method (e.g., the xe2x80x9c1/Exe2x80x9d or xe2x80x9cExe2x80x9d model), by which the lifetime is predicted from the critical injected hole quantity or stress electric field, the lifetime of the insulating film can be predicted more accurately. As a result, the reliability of the semiconductor device can be tested more appropriately.